We draw upon work in learning embeddings for computer vision [1]} to characterize embedding spaces across TSP sizes according to:
(1) magnitudes, denoted by \(\ell _2\)  norms, indicating whether embeddings are shrinking to one magnitude or expanding outwards as TSP size increases;
and (2) pair-wise distances, which tells us how well-separated the embedding are, or whether they are pulled apart/towards each other as TSP size increases.
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